Australia's tax system has become skewed towards a growing and apparently untouchable group of 'taxed nots' - they are older Australians who pay roughly $1 billion per year less tax than younger Australians in the same circumstances, according to a new Grattan Institute report.

Male mining engineers, school principals, surgeons and anaesthetists will be the biggest beneficiaries of the high-end tax cut currently before the Senate, with men more than twice as likely to benefit as women.

The Turnbull government is considering a radical shakeup of Australia's superannuation system that would pit banks and industry funds against each other for the right to manage the deposits of every new entrant for at least two years.